Rate of adsoiption

The rate of adsoiption of species A onto a solid surface. 

Temperature increases the rate of diffusion through the liquid to the adsoiption sites but since the adsoiption process is exothermic, increases in temperature may reduce the degree of adsoiption. This temperature effect is negligible in water-treatment applications and ambient vapor-phase applications. 

The net rate of adsorption is equal to the attachment rate minus the detachment one. Taking into account that the ratio KA = k,Jk A is the adsoiption equilibrium constant, we obtain the following ... 

In the case of dissociative adsoiption, the adsorption rate takes another form. Since two adjacent vacant active sites are required for the molecule to adsorb, the rate of attachment is proportional to the square of the vacant sites concentration. The rate of detachment is now proportional to the product of the occupied sites concentration. Thus... 

Polymer Adsorption. A review of the theory and measurement of polymer adsorption points out succinctly the distinquishing features of the behavior of macromolecules at solid - liquid interfaces (118). Polymer adsoiption and desorption kinetics are more complex than those of small molecules, mainly because of the lower diffusion rates of polymer chains in solution and the "rearrangement" of adsorbed chains on a solid surface, characterized by slowly formed, multi-point attachments. The latter point is one which is of special interest in protein adsoiption from aqueous solutions. In the case of proteins, initial adsoiption kinetics may be quite rapid. However, the slow rearrangement step may be much more important in terms of the function of the adsorbed layer in natural processes, such as thrombogenesis or biocorrosion / biofouling caused by cell adhesion. 

In the above-mentioned cases of polymerization of lower alkyf acrylates, because of the high rate of the process = 1260 dm mol sec for MA (Bagdasar yan, 1966) and the high monomer concentration in particles (Gerrens, 1964), the surface of the monomer-polymer phase increases at a rate that may exceed the rate of attainment of equilibrium adsoiption. 

Because of the quick adsoiption of R+AT molecules on the catalyst surface in the riser inlet zone, the formation rate of is much greater than that of... 

This type of behavior has been demonstrated by Haag for H-ZSM-5 systems and by Lunsford and coworkers for mordenites and faujasites. Both groups reported linear correlations between the cracking rate of n-hexane and the aluminum content of the zeolites. Other studies by Gorte and cowoikers involving the adsoiption of weak bases. 

Die most important property of adsorbent materials, the property tliat is decisive for the adsorbent s usage, is the pore stincture. The total number of pores, their shape, and size deteiniine tlie adsoiption capacity and even the dynamic adsoiption rate of the material. Generally, pores are divided into macro-, iiieso- and micropores. According to lUPAC, pores are classified as shown in Table 2.2. 

A significant feature of physical adsoiption is that the rate of the phenomenon is generally too high and consequently, the overall rate is controlled by mass (or heat transfer) resistance, rather than by the intrinsic soiption kinetics (Ruthven, 1984). Thus, soiption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

In this expression, U(t) is relative rate of uptake and C is relative to equilibrium, i.e. the sites available for ion exchange or adsoiption for the specified ratio V/m. Thus, the absolute rate is a coupled result of kinetics and equilibrium. Note that in a solid diffusion-controlled process, U(t) is relative to the ease of movement of the incoming species in the solid phase (through D ). 

Equilibrium Tlie physical process (reaction) of adsoiption or ion exchange is considered to be so fast relative to diffusion steps tliat in and neai the solid paiticles, a local equilibrium exists. Tlien, tlie so-called adsoiption isotlierm of the form q = f(Cff relates the stationaiy and mobile-phase concentrations at equilibrium. Tlie smface equilibrium relationship between tlie solute in solution and on tlie solid smface can be described by simple analytical equations (see Section 4.1.4). Tlie material balance, rate, and equilibrium equations should be solved simultaneously using tlie appropriate initial and boundary conditions. Tliis system consists of foiu equations and four unknown paianieters (C, q, q, and Q). 

Dalai and coworkers studied the adsoiption/oxidation of MM on Hydrodacro activated carbon. The experiments were carried out at elevated temperatures (323 48 K) at the pressure range between 122 and 364 kPa with the various contents of oxygen (O2/CH3SH ifom 1.1 to 1.33 times the stoichiometry ratio) [132]. At these conditions DMDS and small amounts of CO2 were formed. While the latter is likely the product of carbon surface oxidation, the conversion rate of MM increased with an increasing temperature and 99% was achieved at 373 K. It was found that... 

As a prelude to the development of kinetic rate expressions for heterogeneous chemical reactions, if A reacts with B, for example, then the next step in the mechanism is ha + Ba, forming an activated complex on the snrface. Each reversible step in the seqnence above is characterized by a forward rate constant adsoiption for adsoiption, with units of mol/area time atm, and a backward rate constant A ,desoiption for desorption, with units of mol/area time. The ratio of these rate constants adsorption/ h, desoiption defines the adsorption/desorption equi-... 

Positive values of AH show the endothermic nature of adsorption. Similar results have been reported for the adsorption of methylene blue by clay [19].The native values of AG indicate the spontaneous nature of adsoiption for methylene blue at 35, 40, 50 and 60 C. The positive values of AS suggest the increased randomness at die solid /solution interface during the adsorption of (fye on coir pith cartion. Equilibrium data at different temperatures for the adsorption of dye on coir pith carbon do not follow the first order kinetic model but follows the second order kinetic model. The second order rate constants were in the range 0.357-0.879g/mgfoiin. 

The mass transfer rate for adsoiption is also inversely proportional to the particle size to a power not less than unity. High mass transfer rales are deniable, since less adsoibent is recpiiied for the same separation. Therefore, the size of the packed hed can be reduced by selecting the analler particle size. Since these two criteria are not conqiatible, trade-oils must be made in the design. 

Cairns and CO-workers [114] expressed the adsoiption rate of propane in hydrogen fluoride solutions by an equation for a third-order reaction with respect to free sites on the platinum surface ... 

NH2, C2H5) into the nitro compound as a rule leads to a decrease in the potential shift of the catalyst, i. e., a weakening of the adsoiption capacity, whereas electron-acceptor substituents (COOH, CHO) increase the potential shift of the catalyst, i.e., intensify the interaction between the adsorbed molecules of the nitro compound and the catalyst surface. The way in which such a charge in adsorption capacity is reflected in the overall rate of the catalytic process depends on the nature of the catalyst and the conditions xmder which the process operates. 

Thus, the analysis of the rate-determining step, as analyzed for heterogeneous processes in Section 3.1.2, is equally applied in adsorption and ion exchange. The only difference is that the diffusion processes in the fluid film and in the particle are followed by physical adsoiption or ion exchange and not by a reaction step as in catalysis. 

The search for a suitable adsorbent is generally the first step in the development of an adsorption process. A practical adsorbent has four primary requirements selectivity, capacity, mass transfer rate, and longterm stability. The lequiiement foi adequate adsoiptive capacity icstiicts the choice of adsorbents to microporous solids with pore diameters ranging from a few tenths to a few tens of nanometers. 

Anpo et al have studied TiOa size-effects on the photocatalytic hydrogenation of methylace-tylene with water (32) and found a dependency of the quantum-yield on TiOa anatase panicle size. The relation between the Ar-BET surface area and panicle size obeys eq. [11a], (Fig. 5), but (Table II in ref 32) with Dr=l.S9 0.07, smaller than the possible minimal value for this case, Df=2.0. Df<2 values are usually interpreted as indicating adsoiption which does not coat the whole surface. For the case of anatase we do not believe that on a single panicle there exists a preferred sub-set for Ar adsorption instead we think that the low Dr value indicates loss of surface area by aggregation, namely that the contact areas between the panicles become inaccessible to the Ar. One cannot therefore use the nominal panicle size as reflecting the size of the aggregate (25). However, some useful information can be extracted as follows Since the quantum yield, d>, reflects the overall reactions rate, we apply eq. [11a] for the relation to particle size ... 

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